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Transverse lines to surfaces over finite fieldsMar 21 2019Apr 08 2019We prove that if $S$ is a smooth reflexive surface in $\mathbb{P}^3$ defined over a finite field $\mathbb{F}_q$, then there exists an $\mathbb{F}_q$-line meeting $S$ transversely provided that $q\geq c\operatorname{deg}(S)$, where $c=\frac{3+\sqrt{17}}{4}\approx ... More

Designing Fully Distributed Consensus Protocols for Linear Multi-agent Systems with Directed GraphsDec 28 2013Aug 20 2014This paper addresses the distributed consensus protocol design problem for multi-agent systems with general linear dynamics and directed communication graphs. Existing works usually design consensus protocols using the smallest real part of the nonzero ... More

Energy loss of charm quarks from $J/ψ$ production in cold nuclear matterDec 15 2013$J/\psi$ suppression in p-A collisions is studied by considering the nuclear effects on parton distribution, energy loss of beam proton and the finial state energy loss of color octet $c\overline{c}$. The leading-order computations for $J/\psi$ production ... More

Improved Sufficient Conditions for Exact Convex Relaxation of Storage-Concerned EDMar 25 2016To avoid simultaneous charging and discharging of storages, complementarity constraints are introduced to storage-concerned economic dispatch (ED), which makes the problem non-convex. This letter concerns the conditions under which the convex relaxation ... More

AI Oriented Large-Scale Video Management for Smart City: Technologies, Standards and BeyondDec 05 2017Deep learning has achieved substantial success in a series of tasks in computer vision. Intelligent video analysis, which can be broadly applied to video surveillance in various smart city applications, can also be driven by such powerful deep learning ... More

Hierarchical Clustering Supported by Reciprocal Nearest NeighborsJul 09 2019Clustering is a fundamental analysis tool aiming at classifying data points into groups based on their similarity or distance. It has found successful applications in all natural and social sciences, including biology, physics, economics, chemistry, astronomy, ... More

Soft modes in two- and eight-direction order-disorder ferroelectricsMar 01 2001The soft modes in the two- and eight-direction order-disorder ferroelectrics are calculated under the mean-field approximation. We find that the conventional method of the pseudospin model to calculate the soft-mode frequency is incorrect, and present ... More

Concepts of Ferrovalley Material and Anomalous Valley Hall EffectApr 20 2016May 03 2016Valleytronics rooted in the valley degree of freedom is of both theoretical and technological importance as it offers additional opportunities for information storage and electronic, magnetic and optical switches. In analogy to ferroelectric materials ... More

Magnetic Ordering Induced Giant Optical Property Change in Tetragonal BiFeO3Aug 17 2015Magnetic ordering, as one of the most important characteristics in magnetic materials, could have significant influence on the band structure, spin dependent transport, and other important properties of materials. Its measurement, especially for the case ... More

Two-dimensional ferroelectric tunnel junction: the case of monolayer In:SnSe/SnSe/Sb:SnSe homostructureJul 06 2018Jun 08 2019Ferroelectric tunnel junctions, in which ferroelectric polarization and quantum tunneling are closely coupled to induce the tunneling electroresistance (TER) effect, have attracted considerable interest due to their potential in non-volatile and low-power ... More

Intelligent Power Control for Spectrum Sharing in Cognitive Radios: A Deep Reinforcement Learning ApproachDec 20 2017Apr 08 2018We consider the problem of spectrum sharing in a cognitive radio system consisting of a primary user and a secondary user. The primary user and the secondary user work in a non-cooperative manner. Specifically, the primary user is assumed to update its ... More

Engineering the magnetic anisotropy of atomic-scale nanostructure under electric fieldAug 17 2015Atomic-scale magnetic nanostructures are promising candidates for future information processing devices. Utilizing external electric field to manipulate their magnetic properties is an especially thrilling project. Here, by careful identifying different ... More

Giant dielectric difference in chiral asymmetric bilayersNov 20 2018Nov 21 2018Twistronics rooted in the twist operation towards bilayer van der Waals crystals is of both theoretical and technological importance. The realize of the correlated electronic behaviors under this operation encourages enormous effort to the research on ... More

OCT segmentation: Integrating open parametric contour model of the retinal layers and shape constraint to the Mumford-Shah functionalAug 08 2018In this paper, we propose a novel retinal layer boundary model for segmentation of optical coherence tomography (OCT) images. The retinal layer boundary model consists of 9 open parametric contours representing the 9 retinal layers in OCT images. An intensity-based ... More

A Constructive Algorithm to Prove P=NPJul 31 2012After reducing the undirected Hamiltonian cycle problem into the TSP problem with cost 0 or 1, we developed an effective algorithm to compute the optimal tour of the transformed TSP. Our algorithm is described as a growth process: initially, constructing ... More

Two-dimensional ferroelectric tunnel junction: the case of SnSeJul 06 2018Ferroelectric tunnel junctions (FTJs) have triggered considerable attention in the advanced applications of non-volatile information devices. However, critical thickness for ferroelectricity limits FTJS towards their applications at the nanoscale. Recently, ... More

Ferroelectricity in Pb(Zr$_{0.5}$Ti$_{0.5}$)O$_{3}$ thin films: critical thickness and 180$^\circ$ stripe domainsJul 02 2004The ferroelectric properties of disorder Pb(Zr$_{0.5}$Ti$_{0.5}$)O$_{3}$ thin films are investigated with Monte Carlo simulations on the basis of a first-principles-derived Hamitonian. It is found that there exists a critical thickness of about three ... More

Energy gaps of atomically precise armchair graphene nanoribbonsJan 07 2016Graphene nanoribbons (GNRs) are one-dimensional (1D) structures that exhibit a rich variety of electronic properties1-17. Therefore, they are predicted to be the building blocks in next-generation nanoelectronic devices. Theoretically, it has been demonstrated ... More

Symmetric and asymmetric optical multi-peak solitons on a continuous wave background in the femtosecond regimeMar 15 2016We study symmetric and asymmetric optical multi-peak solitons on a continuous wave background in the femtosecond regime of a single-mode fiber. Key characteristics of such multi-peak solitons, as the formation mechanism, propagation stability, and shape-changing ... More

Electrically tunable polarizer based on two-dimensional orthorhombic ferrovalley materialsJun 20 2017The concept of ferrovalley materials has been proposed very recently. The existence of spontaneous valley polarization, resulting from ferromagnetism, in such hexagonal two-dimensional materials makes nonvolatile valleytronic applications realizable. ... More

Nuclear geometry effect and transport coefficient in semi-inclusive lepton-production of hadrons off nucleiNov 03 2015Hadron production in semi-inclusive deep-inelastic scattering of leptons from nuclei is an ideal tool to determine and constrain the transport coefficient in cold nuclear matter. The leading-order computations for hadron multiplicity ratios are performed ... More

Quark energy loss and shadowing in nuclear Drell-Yan processAug 16 2004The energy loss effect in nuclear matter is another nuclear effect apart from the nuclear effects on the parton distribution as in deep inelastic scattering process. The quark energy loss can be measured best by the nuclear dependence of the high energy ... More

Use of Non-Orthogonal Multiple Access in Dual-hop relayingApr 05 2016Apr 13 2016To improve the sum-rate (SR) of the dual-hop relay system, a novel two-stage power allocation scheme with non-orthogonal multiple access (NOMA) is proposed. In this scheme, after the reception of the superposition coded symbol with a power allocation ... More

Late afterglow emission statistics: a clear link between GW170817 and bright short GRBsJan 06 2019GW170817, the first neutron star merger event detected by advanced LIGO/Virgo detectors, was associated with an underluminous short duration GRB 170817A. In this work we compare the forward shock afterglow emission of GW170817/GRB 170817A to other luminous ... More

A normal-pressure MWPC for beam diagnostics at RIBLL2May 22 2013A normal pressure MWPC for beam diagnostics at RIBLL2 has been developed, which has a sensitive area of 80 mm$\times$80 mm and consists of three-layer wire planes. The anode plane is designed with a wider frame to reduce the discharge and without using ... More

First-principles studies of multiferroic and magnetoelectric materialsAug 29 2015Multiferroics are materials where two or more ferroic orders coexist owing to the interplay between spin, charge, lattice and orbital degrees of freedom. The explosive expansion of multiferroics literature in recent years demon-strates the fast growing ... More

Compact Descriptors for Video Analysis: the Emerging MPEG StandardApr 26 2017This paper provides an overview of the on-going compact descriptors for video analysis standard (CDVA) from the ISO/IEC moving pictures experts group (MPEG). MPEG-CDVA targets at defining a standardized bitstream syntax to enable interoperability in the ... More

Heterogeneous information network model for equipment-standard systemMar 07 2017Entity information network is used to describe structural relationships between entities. Taking advantage of its extension and heterogeneity, entity information network is more and more widely applied to relationship modeling. Recent years, lots of researches ... More

Electrically tunable multiple Dirac cones in thin films of (LaO)2(SbSe2)2 family of materialsSep 12 2014Oct 20 2015Two-dimensional Dirac physics has aroused great interests in condensed matter physics ever since the discovery of graphene and topological insulators due to its importance in both fundamental physics and device applications. The ability to control the ... More

Generating Giant and Tunable Nonlinearity in a Macroscopic Mechanical Resonator from Chemical Bonding ForceJun 24 2015Nonlinearity in macroscopic mechanical system plays a crucial role in a wide variety of applications, including signal transduction and processing, synchronization, and building logical devices. However, it is difficult to generate nonlinearity due to ... More

Fast MPEG-CDVS Encoder with GPU-CPU Hybrid ComputingMay 27 2017Jun 09 2017The compact descriptors for visual search (CDVS) standard from ISO/IEC moving pictures experts group (MPEG) has succeeded in enabling the interoperability for efficient and effective image retrieval by standardizing the bitstream syntax of compact feature ... More

On the Borel transgression in the fibration $G\rightarrow G/T$Oct 09 2017Let $G$ be a semisimple Lie group with a maximal torus $T$. We present an explicit formula for the Borel transgression $\tau :H^{1}(T)\rightarrow H^{2}(G/T)$ of the fibration $G\rightarrow G/T$. This formula corrects an error in the paper \cite{K}, and ... More

On the inverse Kostka matrixJun 13 2003We present both a combinatorial characterization and a recurrent formula for the entries of the inverse Kostka matrix. An application to the topology of the classifying space BU(n) is obtained.

A quantum gravity tensor equation formally integrating general relativity with quantum mechanicsJun 09 2016Extending black-hole entropy to ordinary objects, we propose kinetic entropy tensor, based on which a quantum gravity tensor equation is established. Our investigation results indicate that if N=1, the quantum gravity tensor equation returns to Schrodinger ... More

The near-Hopf ring structure on the integral cohomology of 1-connected Lie groupsAug 29 2010Sep 03 2010Let G be an exceptional Lie group with a maximal torus T. Based on Schubert calculus on the flag manifold G/T we have described the integral cohomology ring H*(G) by explicitely constructed generators in [DZ2], and determined the structure of H*(G;F_{p}) ... More

Transverse lines to surfaces over finite fieldsMar 21 2019We prove that if $S$ is a smooth reflexive surface in $\mathbb{P}^3$ defined over a finite field $\mathbb{F}_q$, then there exists an $\mathbb{F}_q$-line meeting $S$ transversely provided that $q\geq c\operatorname{deg}(S)$, where $c=\frac{3+\sqrt{17}}{4}\approx ... More

Dynamic Modulation of the Transport Properties of the LaAlO3/SrTiO3 Interface Using Uniaxial StrainJul 11 2016Among the interfacial transport modulations to the LaAlO3/SrTiO3 (LAO/STO) heterostructure, mechanical strain has been proven to be an effective approach by growing the LAO/STO films on different substrates with varying lattice mismatches to STO. However, ... More

Schubert calculus and cohomology of Lie groups. Part II. Compact Lie groupsFeb 02 2015Apr 15 2016Let $G$ be a compact Lie group with a maximal torus $T$. Based on a presentation of the integral cohomology ring $H^{\ast}(G/T)$ of the flag manifold $G/T$ in \cite{DZ1}we have presented in \cite{DZ2}an explicit and unified construction of the integral ... More

Passive Tracer Dispersion with Random or Periodic SourceMay 25 1998In this paper, the author investigates the impact of external sources on the pattern formation and long-time behavior of concentration profiles of passive tracers in a two-dimensional shear flow. It is shown that a time-periodic concentration profile ... More

A K-theory approach to the tangent invariants of blow-upsDec 14 2013We extend the formula for the Chern classes of blow-ups of algebraic varieties due to Porteous and Lascu-Scott, and of symplectic and complex manifolds due to Geiges and Pasquotto, to the blow-ups of almost complex manifolds. Our approach is based on ... More

Predictability in Spatially Extended Systems with Model UncertaintyDec 18 2008Mar 26 2009Macroscopic models for spatially extended systems under random influences are often described by stochastic partial differential equations (SPDEs). Some techniques for understanding solutions of such equations, such as estimating correlations, Liapunov ... More

Predictability in Nonlinear Dynamical Systems with Model UncertaintyNov 22 2008Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic differential ... More

Testing the Universality of Free Fall at ${10^{ - 10}}$ level by Comparing the Atoms in Different Hyperfine States with Bragg DiffractionMay 20 2018May 31 2018We have performed a precision atomic interferometry experiment on testing the universality of free fall (UFF) considering atoms' spin degree of freedom. Our experiment employs the Bragg atom interferometer with $^{87}$Rb atoms either in hyperfine state ... More

Test of the universality of free fall with atoms in different spin orientationsFeb 20 2016We report a test of the universality of free fall (UFF) by comparing the gravity acceleration of the $^{87}$Rb atoms in $m_F=+1$ versus that in $m_F=-1$, where the corresponding spin orientations are opposite. A Mach-Zehnder-type atom interferometer is ... More

Deterministic Role of Concentration Surplus of Cation Vacancy over Anion Vacancy in Bipolar Memristive NiOJan 29 2017Migration of oxygen vacancies has been proposed to play an important role in the bipolar memristive behaviors since oxygen vacancies can directly determine the local conductivity in many systems. However, a recent theoretical work demonstrated that both ... More

Manipulation of the large Rashba spin splitting in polar two-dimensional transition metal dichalcogenidesJun 26 2016Feb 20 2017Transition metal dichalcogenide (TMD) monolayers MXY (M=Mo, W, X(not equal to)Y=S, Se, Te) are two-dimensional polar semiconductors. Setting WSeTe monolayer as an example and using density functional theory calculations, we investigate the manipulation ... More

Flavor Oscillation Modes In Dense Neutrino MediaSep 27 2013Nov 13 2013We study two-flavor neutrino oscillations in homogeneous neutrino gases in which neutrinos and anti-neutrinos are in nearly pure weak interaction states initially. We find that the monopole and dipole oscillation modes can trigger flavor instabilities ... More

The cohomology of the projective unitary groupsOct 25 2017Dec 20 2017The projective unitary group $PU(n)$ is the quotient group of the unitary group $U(n)$ by its center $S^{1}$. We determine the integral cohomology ring $H^{\ast }(PU(n))$ using explicitly constructed generators.

Magnetohydrodynamic regime of the born-infeld electromagnetismJun 06 2017The Born-Infeld (BI) model is a nonlinear correction of Maxwell's equations. By adding the energy and Poynting vector as additional variables, it can be augmented as a 10$\times$10 system of hyperbolic conservation laws, called the augmented BI (ABI) ... More

Multiplicative rule of Schubert classesJun 15 2003Sep 01 2003Let G be a compact connected Lie group and H, the centralizer of a one-parameter subgroup in G. Combining the ideas of Bott-Samelson resulotions of Schubert varieties and the enumerative formula on a twisted products of 2-spheres obatained in {Du2], we ... More

A Problem of Hsiang-Palais-Terng on isoparametric submanifoldsDec 12 2003We solve the problem raised by Hsiang, Palais and Terng in [The topology of isoparametric submanifolds, JDG, 27(1988), 423-460]: Is it possible to have an isoparametric foliation on R^{52} whose marked Dynkin giagram is of type D_4 and with all multiplicities ... More

A homotopy aspect of representation theoryFeb 14 2005Mar 10 2005We bring a linkage from representation theory of Lie groups to homotopy theory for maps between flag manifolds. As applications we derive from representation theory abundant families of homotopy classes of maps between flag manifolds whose induced cohomology ... More

A Remark on the Three Dimensional Baroclinic Quasigeostrophic DynamicsJun 03 1998We consider time-periodic patterns of the dissipative three dimensional baroclinic quasigeostrophic model in spherical coordinates, under time-dependent forcing. We show that when the forcing is time-periodic and the spatial square-integral of the forcing ... More

Time-Periodic Quasigeostrophic Motion under Dissipation and ForcingMay 25 1998The quasigeostrophic equation is a prototypical geophysical fluid model. In this paper, we consider time-periodic motions of this model under dissipation and time-dependent wind forcing. We show that when the wind forcing is time-periodic and the spatial ... More

The characteristic classes and Weyl invariants of Spinor groupsOct 09 2018Jul 03 2019Based on a pair of cohomology operations on so called $\delta-2$-formal spaces, we construct the integral cohomology rings of the classifying spaces of the Lie groups $Spin(n)$ and $Spin^{c}(n)$. As applications, we introduce characteristic classes for ... More

Stochastic Modeling of Unresolved Scales in Complex SystemsNov 22 2008Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or limitations ... More

Terahertz and Far-Infrared Windows Opened at Dome A, AntarcticaSep 20 2016The terahertz and far-infrared (FIR) band, from approximately 0.3 THz to 15 THz (1 mm to 20 micron), is important for astrophysics as the thermal radiation of much of the universe peaks at these wavelengths and many spectral lines that trace the cycle ... More

Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body SystemsAug 11 2015May 22 2016This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring ... More

Adaptive Low-Nonnegative-Rank Approximation for State Aggregation of Markov ChainsOct 14 2018This paper develops a low-nonnegative-rank approximation method to identify the state aggregation structure of a finite-state Markov chain under an assumption that the state space can be mapped into a handful of meta-states. The number of meta-states ... More

Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body SystemsAug 11 2015Feb 23 2018This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring ... More

Surface symmetry breaking and disorder effects on superconductivity in perovskite BaBi3 epitaxial filmsAug 22 2018The structural or electronic symmetry breaking of the host lattice is a recurrent phenomenon in many quantum materials, including superconductors. Yet, how these broken symmetry states affect the electronic pair wave function of superconductivity have ... More

Prolific interaction structures and shape-changing collisions in an erbium-doped fiber systemJan 13 2016Jan 20 2016Prolific interactions of nonlinear waves on a plane-wave background in an erbium-doped fiber system are unveiled, based on explicit coexistence conditions extracting from the general higher-order solution of a coupled nonlinear Schr\"odinger and the Maxwell-Bloch ... More

Transfer Metric Learning: Algorithms, Applications and OutlooksOct 09 2018Nov 12 2018Distance metric learning (DML) aims to find an appropriate way to reveal the underlying data relationship. It is critical in many machine learning, pattern recognition and data mining algorithms, and usually require large amount of label information (such ... More

Known-class Aware Self-ensemble for Open Set Domain AdaptationMay 03 2019Existing domain adaptation methods generally assume different domains have the identical label space, which is quite restrict for real-world applications. In this paper, we focus on a more realistic and challenging case of open set domain adaptation. ... More

Coexistence of spin glass and ferroelectricity in highly ordered Bi2FeMnO6 epitaxial thin filmDec 20 2015Jan 17 2016Highly ordered Bi2FeMnO6 epitaxial thin films have been successfully grown on SrTiO3 substrate. Both synchrotron X-ray reciprocal space mapping and high resolution transmission electron microscopy confirmed the alternative alignment of Fe and Mn along ... More

Global quantum discord in infinite quantum spin chainsDec 17 2014In this paper, we study global quantum discord (GQD) in infinite-size spin chains. For this purpose, in the framework of matrix product states (MPSs), we propose an effective procedure to calculate GQD (denoted as Gn) for consecutive n-site subchains ... More

Coverless information hiding based on Generative ModelFeb 10 2018A new coverless image information hiding method based on generative model is proposed, we feed the secret image to the generative model database, and generate a meaning-normal and independent image different from the secret image, then, the generated ... More

A unified formula for Steenrod operations in flag manifoldsJun 17 2003Feb 14 2005The classical Schubert cells on a flag manifold G/H give a cell decomposition for G/H whose Kronecker duals (known as Schubert classes) form an additive base for the integral cohomology H^{\ast}(G/H). We present a formula that expresses Steenrod mod-p ... More

Dynamic Pricing and Capacity Allocation of UAV-provided Mobile ServicesDec 07 2018Due to its agility and mobility, the unmanned aerial vehicle (UAV) is a promising technology to provide high-quality mobile services (e.g., fast Internet access, edge computing, and local caching) to ground users. Major Internet Service Providers (ISPs) ... More

Fast neutrino flavor conversion: roles of dense matter and spectrum crossingDec 19 2017Aug 17 2018The flavor conversion of a neutrino usually occurs at densities $\lesssim G_F^{-1} \omega$, whether in the ordinary matter or the neutrino medium, and on time/distance scales of order $\omega^{-1}$, where $G_F$ is the Fermi weak coupling constant and ... More

Applying Supervised Learning Algorithms and a New Feature Selection Method to Predict Coronary Artery DiseaseFeb 03 2014From a fresh data science perspective, this thesis discusses the prediction of coronary artery disease based on genetic variations at the DNA base pair level, called Single-Nucleotide Polymorphisms (SNPs), collected from the Ontario Heart Genomics Study ... More

Schubert calculus and the Hopf algebra structures of exceptional Lie groupsMar 26 2009Aug 29 2010Let G be an exceptional Lie group with a maximal torus T. Based on common properties in the Schubert presentation of the cohomology ring H*(G/T;F_{p}) DZ1, and concrete expressions of generalized Weyl invariants for G over F_{p}, we obtain a unified approach ... More

Schubert presentation of the integral cohomology ring of the flag manifolds G/TJan 16 2008Feb 08 2015Let G be a compact connected Lie group with a maximal torus T\subsetG. In the context of Schubert calculus we obtain a canonical presentation for the integral cohomology ring H^{\ast}(G/T) of the complete flag manifold G/T. The result have been applied ... More

Schubert calculus and cohomology of Lie groups. Part I. 1-connected Lie groupsNov 16 2007Sep 10 2015Let $G$ be a compact and $1$--connected Lie group with a maximal torus $T$. Based on Schubert calculus on the flag manifold $G/T$ [15] we construct the integral cohomology ring $H^{\ast}(G)$ uniformly for all $G$.

The Chow rings of generalized GrassmanniansNov 14 2005Aug 08 2008Based on the Basis theorem of Bruhat--Chevalley [C] and the formula for multiplying Schubert classes obtained in [D\QTR{group}{u}] and programed in [DZ$_{\QTR{group}{1}}$], we introduce a new method computing the Chow rings of flag varieties (resp. the ... More

Algorithm for multiplying Schubert classesSep 09 2003Oct 22 2005Based on the multiplicative rule of Schubert classes obtained in [Du3], we present an algorithm computing the product of two arbitrary Schubert classes. As a result, the algorithm gives also a method to compute the integral cohomology ring of a flag manifold ... More

Stochastic Power System Simulation Using the Adomian Decomposition MethodOct 06 2017For dynamic security assessment considering uncertainties in grid operations, this paper proposes an approach for time-domain simulation of a power system having stochastic loads. The proposed approach solves a stochastic differential equation model of ... More

Statistical analysis of the limitation of half integer resonances on the available momentum acceptance of a diffraction-limited storage ringJun 23 2016In a diffraction-limited storage ring (DLSR), the momentum acceptance (MA) might be limited by the half integer resonances (HIRs) excited by focusing errors, associated with the large detuning terms from the strong focusing and strong sextupoles required ... More

Slowing light with a coupled optomechanical crystal arrayFeb 09 2012We study the propagation of light in a resonator optical waveguide consisting of evanescently coupled optomechanical crystal array. In the strong driving limit, the Hamiltonian of system can be linearized and diagonalized. In this case we obtain the polaritons, ... More

A hierarchical random compression method for kernel matricesMar 13 2018In this paper, we propose a hierarchical random compression method (HRCM) for kernel matrices in fast kernel summations. The HRCM combines the hierarchical framework of the H-matrix and a randomized sampling technique of the column and row spaces for ... More

A linear-time algorithm for generalized trust region subproblemsJul 19 2018May 06 2019In this paper, we provide the first provable linear-time (in the number of non-zero entries of the input) algorithm for approximately solving the generalized trust region subproblem (GTRS) of minimizing a quadratic function over a quadratic constraint ... More

Quantifying Uncertainties in Complex SystemsDec 01 2009Jul 20 2010Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by observations. The ... More

A Stochastic Approach for Parameterizing Unresolved Scales in a System with MemoryJan 21 2009Complex systems display variability over a broad range of spatial and temporal scales. Some scales are unresolved due to computational limitations. The impact of these unresolved scales on the resolved scales needs to be parameterized or taken into account. ... More

High-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamicsMay 15 2019This paper develops the high-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamic equations. The schemes are built on the entropy conservative flux and the weighted essentially non-oscillatory ... More

Impacts of Noise on a Class of Partial Differential EquationsFeb 25 2014Oct 11 2014This paper is concerned with effects of noise on the solutions of partial differential equations. We first provide a sufficient condition to ensure the existence of a unique positive solution for a class of stochastic parabolic equations. Then, we prove ... More

Large deviations for the Boussinesq Equations under Random InfluencesFeb 10 2008Nov 07 2008A Boussinesq model for the Benard convection under random influences is considered as a system of stochastic partial differential equations. This is a coupled system of stochastic Navier-Stokes equations and the transport equation for temperature. Large ... More

On the non-degeneracy of radial vortex solutions for a coupled Ginzburg-Landau systemMay 01 2019For the following Ginzburg-Landau system in ${\mathbb R}^2$ \begin{align*} \begin{cases} -\Delta w^+ +\Big[A_+\big(|w^+|^2-{t^+}^2\big)+B\big(|w^-|^2-{t^-}^2\big)\Big]w^+=0, \\[3mm] -\Delta w^- +\Big[A_-\big(|w^-|^2-{t^-}^2\big)+B\big(|w^+|^2-{t^+}^2\big)\Big]w^-=0, ... More

Distributed Adaptive Attitude Synchronization of Multiple SpacecraftFeb 28 2011Jun 10 2011This paper addresses the distributed attitude synchronization problem of multiple spacecraft with unknown inertia matrices. Two distributed adaptive controllers are proposed for the cases with and without a virtual leader to which a time-varying reference ... More

Dynamic Pricing for Controlling Age of InformationApr 02 2019Apr 03 2019Fueled by the rapid development of communication networks and sensors in portable devices, today many mobile users are invited by content providers to sense and send back real-time useful information (e.g., traffic observations and sensor data) to keep ... More

Economic Analysis of Rollover and Shared Data PlansMar 29 2019In today's growing data market, wireless service providers (WSPs) compete severely to attract users by announcing innovative data plans. Two of the most popular innovative data plans are rollover and shared data plans, where the former plan allows a user ... More

Strings and the Gauge Theory of Spacetime DefectsSep 07 1998Oct 08 1998we present a new topological invariant to describe the space-time defect which is closely related to torsion tensor in Riemann-Cartan manifold. By virtue of the topological current theory and $\phi$-mapping method, we show that there must exist many strings ... More

Harmonic field in knotted spaceApr 26 2018Knotted fields enrich a variety of physical phenomena, ranging from fluid flows, electromagnetic fields, to textures of ordered media. Maxwell's electrostatic equations, whose vacuum solution is mathematically known as a harmonic field, provide an ideal ... More

Fokker-Planck equations for nonlinear dynamical systems driven by non-Gaussian Levy processesFeb 12 2012The Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and are thus widely used to quantify random phenomena such as uncertainty propagation. For dynamical systems driven by non-Gaussian L\'evy processes, ... More

Asymptotic methods for stochastic dynamical systems with small non-Gaussian Lévy noiseJan 04 2012Feb 17 2014The goal of the paper is to analytically examine escape probabilities for dynamical systems driven by symmetric $\alpha$-stable L\'evy motions. Since escape probabilities are solutions of a type of integro-differential equations (i.e., differential equations ... More

State space decomposition for nonautonomous dynamical systemsMar 26 2009Decomposition of state spaces into dynamically different components is helpful for the understanding of dynamical behaviors of complex systems. A Conley type decomposition theorem is proved for nonautonomous dynamical systems defined on a non-compact ... More

The 3D Quasigeostrophic Fluid Dynamics under Random Forcing on BoundaryDec 30 2000The three-dimensional baroclinic quasigeostrophic flow model has been widely used to study basic mechanisms in oceanic flows and climate dynamics. In this paper, we consider this flow model under random wind forcing and time-periodic fluctuations on fluid ... More

Separation between quantum Lovász number and entanglement-assisted zero-error classical capacityAug 16 2016Quantum Lov\'asz number, as a natural generalization of the celebrated Lov\'asz number in graph theory, is the best known efficiently computable upper bound of the entanglement-assisted zero-error classical capacity of a quantum channel. However, it remains ... More

Second Order Cone Constrained Convex Relaxations for Nonconvex Quadratically Constrained Quadratic ProgrammingAug 06 2016Sep 16 2017In this paper, we present new convex relaxations for nonconvex quadratically constrained quadratic programming (QCQP) problems. While recent research has focused on strengthening convex relaxations using reformulation-linearization technique (RLT), the ... More

The Boltzmann Equation with Large-amplitude Initial Data in Bounded DomainsMar 23 2017Nov 13 2018The paper is devoted to constructing the global solutions around global Maxwellians to the initial-boundary value problem on the Boltzmann equation in general bounded domains with isothermal diffuse reflection boundaries. We allow a class of non-negative ... More

The index quasi-periodicity and multiplicity of closed geodesicsAug 09 2010Aug 22 2010In this paper, we prove the existence of at least two distinct closed geodesics on every compact simply connected irreversible or reversible Finsler (including Riemannian) manifold of dimension not less than 2.